I need your help with creating a porous structure in Grasshopper based on Voronoi tessellation. The structure I have developed so far can be seen in the pictures below, including the corresponding Grasshopper file.

I have got 2 specific questions:

How can you determine the volume of the structure in order to calculate the percentage of porosity? I used the Volume and the Mass Addition components to determine the mass of the (bounding)box. However, I was unable to do this for the rod-like structure within the box.

Is it possible to make this structure fully solid in Grasshopper? As can been seen in the picture, the rods are defined by the surfaces but I would like a closed and solid structure in the end. This way I can directly export it as .stl and start 3D printing.

Hello
it is doable to make the cuts, but at the moment Rhino/Grasshopper are not very good at that.
Here a solution using Dendro. There are many ways with Dendro to make smooth nodes/sponge.

Thank you very much for your suggestions and your alternative approach also looks very nice!
However, my goal is to investigate the influence of the scaling factors on the percentage porosity. So I want to keep that method.

I was able to create a closed mesh, see the picture and file below. Unfortunately, calculating the volume of the structure (with Mesh Volume still results in the error: Mesh geometry is not solid!. So I tried the method of intersecting the skeletal mesh with a solid object using the Dendro plug-in, but was not successful…

Thank you for the suggestions! Indeed, I though closing the mesh would solve both problems.
In the end I was able to close the holes using a different method, resulting in the structure below. However, the calculation of the percentage porosity turns out to not work because I still have difficulties determining the volume of the structure (using Mesh Volume results in the error: Mesh geometry is not solid!).

Do you have an suggestion to end up with a solid geometry?
Hopefully, you can open the Grasshopper file.

this is just a small hint, but by scaling down the original mesh box by a tiny fraction the mesh intersection works (you already get a closed mesh)
it worked for me (Rhino 7 update 12/08/2020) for any amount of voronoi points